Control of Uncertain Systems with Bounded Inputs by Sophie Tarbouriech, Germain Garcia

By Sophie Tarbouriech, Germain Garcia

In sensible keep watch over difficulties, many constraints must be dealt with which will layout controllers which function in a true atmosphere. by way of combining effects on strong keep watch over and saturating keep watch over, this booklet makes an attempt to supply confident aid for sensible events and, as one of many first books to merge the 2 keep an eye on fields, it may generate massive curiosity in scientific/acad emic circles. the 10 chapters, which care for stabilization and keep an eye on of either linear and nonlinear structures, are every one self sustaining of their procedure - a few deal in basic terms with theoretical effects while others pay attention to ways that the speculation could be utilized. The book's cohesion is secured through the need to formulate keep watch over layout specifications via constraints on enter and version uncertainty description.

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52 Anthony N. Michel and Ling Hou E x a m p l e 2. 1). Since n = 3 in the present case, there are 22n-1= 32 matrices to be checked. We used MATLAB to generate the 32 matrices AI, J,tJ from Am to A M and to verify the positive definiteness of the matrices P A IIg , j , + ( A FtJj , )TP. 6966 which turns out to be the smallest eigenvalue among all the PAI,j,+(AI, ) l g IJj, Tp involved. 1) with A m and A M given above is globally asymptotically stable. , [2]). [] 6. C o n c l u d i n g Remarks We established new sufficient conditions for the global asymptotic stability of the trivial solution of uncertain systems described by ordinary differential equations under complete saturation constraints (where all states are subject to saturation constraints) and systems with partial saturation constraints (where some of the states are subject to saturation constraints).

N, z e D " } and let d = min{di,i = 1 , . - . , n } . Let ~t = { x i , - - . i,,,rdrfti,H~ii(to ) for all t E [to, to + d/M). 1). It follows from the foregoing argument that in (to,to+d/M), [xi(t)l < 1 for all iE { 1 , . . , r } , and xi = hx,(~']~=laijxj) = ~'~'=1 aijxj. For iE { r + l , . . (fii,,I)X-l(t- to)XAI,H2n(to)) + [ai(r+l),"" ", ain]~2II(to) ---- [ail,'' ", ain]x(to) + E),°°=l l [ a i l , - - - , alr](AI,l) ~-1 × ± ~ + ' ~(to) "---- E A = 0 dt x A! 0. - , n}, it follows from the choice ofd that &~ = h x, (~-~j=l a~jxj) = " 0.

Ence. 4) 50 Anthony N. 4) r~ is negative definite for all (x T,yT)T E R (n-m) × Dm. In view of the assumptions on P1 and P2, it follows that V is also positive definite and radially unbounded on R (~-m) x D "~. ~ ¢(r) = ~ ) . Now let s~ = {z = (x ~, yT)T e R("-m) × D m : V(z) < c} and note that for any solution z(t, zo,to = O) = z(t) = (x(t) T, y(t)) T with z(0) = z0, there exists a c > 0 such that z0 E So. 1 to show that the equilibrium ze = 0 is globally asymptotically stable. 1 did not depend on the particular form of the compact set Din).

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